It certainly is. The average UK household owns £35,000 worth of stuff. That's going to cost a lot to replace if it's damaged, lost or stolen. So, while you're not legally obligated to take out contents insurance, not doing so could be risky.
And if you already have contents insurance, check whether it covers your belongings while they’re in transit from your old house to your new one. Some policies include this as standard, and some allow you to add it on. In either case, you'll likely need to use a proper removal firm, otherwise you won't be covered while you’re moving your possessions to your new house.
You may be able to benefit from the removal firm’s insurance. That way, if you do need to make a claim, it won't affect your insurance premium or no claims bonus. And you might not have to pay an excess charge either.
If you don't have contents insurance, it’s a worthwhile consideration before your big move. Again, shop around so you know you’re getting the right deal for the level of cover you need.